

A361856


Positive integers whose prime indices satisfy (maximum) = 2*(median).


19



12, 24, 42, 48, 60, 63, 72, 96, 126, 130, 140, 144, 189, 192, 195, 252, 266, 288, 308, 325, 330, 360, 378, 384, 399, 420, 432, 495, 546, 567, 572, 576, 588, 600, 630, 638, 650, 665, 756, 768, 819, 864, 882, 884, 931, 945, 957, 962, 975, 1122, 1134, 1152, 1190
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OFFSET

1,1


COMMENTS

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
The median of a multiset is either the middle part (for odd length), or the average of the two middle parts (for even length).
These are Heinz numbers of partitions satisfying (maximum) = 2*(median).


LINKS



FORMULA



EXAMPLE

The terms together with their prime indices begin:
12: {1,1,2}
24: {1,1,1,2}
42: {1,2,4}
48: {1,1,1,1,2}
60: {1,1,2,3}
63: {2,2,4}
72: {1,1,1,2,2}
96: {1,1,1,1,1,2}
126: {1,2,2,4}
130: {1,3,6}
140: {1,1,3,4}
144: {1,1,1,1,2,2}
The prime indices of 126 are {1,2,2,4}, with maximum 4 and median 2, so 126 is in the sequence.
The prime indices of 308 are {1,1,4,5}, with maximum 5 and median 5/2, so 308 is in the sequence.


MATHEMATICA

prix[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], Max@@prix[#]==2*Median[prix[#]]&]


CROSSREFS

The LHS (greatest prime index) is A061395.
These partitions are counted by A361849.
A000975 counts subsets with integer median.


KEYWORD

nonn


AUTHOR



STATUS

approved



